Optical communications systems operate at the limits of their margins to respond to increasing capacity demands. Some of the signal processing functions required must soon operate at speeds beyond electronic implementation. Optical signal processors are fundamentally analog which requires precise control of the operating state. Programmable optical components are consequently essential. The thesis explores and elucidates the properties of meshes of generalized Mach-Zehnder interferometers (GMZIs) amenable to silicon (Si) photonics integration that are based on multimode interference couplers with programmability achieved via voltage controlled phase-shift elements within the interferometer arms to perform a variety of finite impulse response (FIR) and infinite impulse response (IIR) signal processing functions. The thesis presents a novel class of integrated photonic phased array systems with a single-stage, multistage, and feedback architectures. The designed photonic integrated systems utilize nano-electromechanical-system (NEMS) operated phase shifters of cascaded free suspended slot waveguides that are compact and require a small amount of power to operate. The structure of the integrated photonic phased array switch (IPPAS) elements is organized such that it brings the NEMS-operated phase shifters to the exterior sides of the construction; facilitating electrical connection. The transition slot couplers used to interconnect the phase shifters to the rest of the silicon structure are designed to enable biasing one of the silicon beams of each phase shifter from an electrode located at the side of the phase shifter. The other silicon beam of each phase shifter is biased through the rest of the silicon structure of the fabric, which is taken as a ground. Phased array processors of 2×2 and 4×4 multiple-input-multiple-output (MIMO) ports are conveniently designed within reasonable footprints native to the current fabrication technologies. The response of the single-stage 4×4 broadband IPPAS element is determined, and its phase synthesis states required for single-throw, double-throw and broadcast routing operations are predicted. The transmission responses of the single-stage wavelength division multiplexing (WDM) processors of 2×2 and 4×4 MIMO ports are simulated. The wavelength steering capability of the transmission interferograms by applying progressive phase shifts through the array of NEMS-operated phase shift elements of the single-stage 4×4 WDM (de)multiplexer is demonstrated. The advantages of cascading broadband and WDM phased array sections are articulated through several study cases. Five different cascaded phased array architectures are trialed for the construction of non-blocking 4×4 IPPAS broadband switches that are essential elements in the construction of universal photonic processors. A cascaded 2×2 WDM (de)multiplexer that can set the bandwidth of the (de)multiplexed cyclic channels into a binary number of programmable values is demonstrated. The envelope and wavelength modulations of the transmission responses utilizing a cascaded forward structure of three 2×2 sections that can be utilized for the (de)multiplexing of different bandwidth channels are demonstrated providing individual wavelength steering capability of the narrowband and wideband channels and the individual wavelength steering capability of the slow envelope and wavelength modulating functions. Innovative universal 2×2 and 4×4 cascaded phased array processors of advanced high-order architectures that can function as both non-blocking broadband routers and tunable WDM (de)multiplexers with spectrum steering and bandwidth control of the (de)multiplexed demands are introduced. The multimode interference (MMI) coupler is utilized for the construction of several IIR feedback photonic processors. Tunable photonic feedback processors have the advantage of using less number of MMI couplers compared to their counterparts of FIR forward-path processors saving on the footprint and loss merits. A passive feedback 2×2 (de)multiplexer made of a 4×4 MMI coupler and two loopback paths is proposed. The inclusion of an imbalance in the lengths of the loopback paths of the same symmetrical feedback (de)multiplexer is demonstrated to achieve wavelength modulation of the (de)multiplexed transmission responses that are useful for the (de)multiplexing of different bandwidth channels. Several newly introduced IIR feedback architectures are demonstrated to function similarly as their counterparts of FIR forward-path processors as binary bandwidth variable (de)multiplexers, envelope and wavelength modulation (de)multiplexers, and universal feedback processors. The investigation provided in this thesis is also supported with dynamic zero-pole evolution analysis in the complex plane of analysis of the studied FIR and IIR photonic processors to enhance understanding the principle of operation. This research expands the prospective for constructing innovative silicon-on-insulator (SOI) based optical processors for applications in modern optical communication systems and programmable elastic optical networks (EONs).

With the advent of micro and nano electromechanical systems (MEMS/NEMS), there has been rapid development in the design and fabrication of sensitive resonant sensors. Sensitivity of such devices depends on the resonant frequency and the quality factor (Q). The Q of these devices are dependent on process induced prestress in the structural geometry, interaction with the external environment, and the encapsulation method. For high frequency sensors operating in air and under encapsulation condition, the Q is dominated by structural and fluid-structure interaction losses. In this thesis, we set out to study the dominant energy dissipative mechanisms that are constituent of the experimentally observed loss (Q-factor) in two specific test geometries—uncapped and capped circular MEMS drumhead resonators. Considering the importance of various factors, we consider four important problems pertaining to the uncapped as well as capped resonators. In the first problem, the most important factors perhaps are the acoustic radiation losses emanating from the annular plate, and the effect of added mass effect on the natural frequencies of the annular plate. The second problem is to investigate the dominant contribution of squeeze film losses and acoustic radiation losses with respect to various natural frequencies of the annular plate. The third problem is to consider the effect of prestress on the natural frequencies of the annular plate and its associated fluid-structure interaction losses (quality factors due to squeeze film damping and acoustic radiation losses). The fourth problem is to study the dominant fluid-structure interaction losses and structural losses that are constituent of experimentally measured Q-factors of the encapsulated annular plate (conceptual representation of MEMS device under packaged conditions). In the first problem, we study the mode dependent acoustic radiation losses in an uncapped drumhead microresonator which is represented by a annular circular plate fixed at its outer edge, suspended over a fixed substrate. There are two main effects which are associated with such systems due to the fluid-structure interaction. First is the “added mass effect,” which reduces the effective resonance frequency of the structure. The second is the acoustic radiation loss from the top side of the resonator, that affects the quality factor of the vibrating structure. In deriving the analytical solution, we first obtain the exact mode shapes of the structure ignoring any effect of the surrounding fluid (air) on the mode shape. Subsequently, we use these mode shapes to study the effect of the surrounding fluid on the associated natural frequencies and the Q-factor. The effect of “added mass” on the frequencies of the structure is found to be negligible. However, the acoustic radiation losses found to be significant. Additionally, we found that the variation in Qac over the first few modes (< 40 MHz) is marked with a local maximum and a minimum. Beyond this range, Qac increases monotonically over the higher frequency modes. It is also found that such kind of variation can be described using different acoustics parameters. Finally, comparing the acoustics radiation loss based quality factor with the experimental results for the uncapped drumhead resonator, the acoustic damping dominates only at higher modes. Therefore, our second problem forms the basis of finding other fluid-related damping. In the second problem, we explore the fluid losses due to squeeze film damping in the uncapped drumhead micro resonator. In this case, the squeeze film loss is due to the flow of the fluid film between the bottom surface of the annular plate and the fixed substrate. Based on the literature survey, it is found that the squeeze film damping reduces with increase in the air-gap thickness and the operating frequencies respectively. However, the squeeze film effect can not be ignored at lower frequencies. In order to investigate the contribution of squeeze film damping in uncapped resonator, we determine squeeze-film damping based quality factor Qsq corresponding to different modes of the resonators using FEM based software, ANSYS. On comparing Qsq with the experiments, we found that Qsq matches well with the experiments corresponding to the lower modes. Therefore, it is found that Qsq dominates at low frequencies (< 20 MHz) and Qac plays significant role at high frequencies (> 40 MHz). Both types of damping should be considered while modeling the fluid damping in uncapped resonator. In the next study, we discuss the effects of prestress on the resonant frequencies and quality factor. In the third study, we discuss the applicability of thin-plate theory with prestress and membrane theory in computing the frequencies and quality factor due to acoustic and squeeze film losses in the uncapped drumhead resonator. In the first two studies, although the quality factor due to acoustic losses and the squeeze film captures the correct trend of the experimental results, there is a mismatch between the experimental and theoretical frequencies computed with added mass effect. In order to improve the computation of frequencies corresponding to measured modes, we first used membrane theory to predict the frequencies, and finally we quantify that there exists discrepancy between computed and the corresponding experimental frequencies with error of about 8–55%. Since, both the membrane as well as thin plate theory without prestress do not correctly model the frequencies, we used the thin plate theory with prestress. For a prestress level of 96 MPa, we found the match between the computed frequencies and the corresponding quality factors with the measured values. However, we also found that there exists strong dependence of prestress on the acoustic radiation loss, with decrease in the acoustic loss based quality factors with increase in the prestress level. In the subsequent problem, we focus on the computation of losses in capped drumhead resonator which leads to a design possibility of improving the quality factor by containing the acoustic radiation losses. In the fourth problem, we study the structural and fluid-structure interaction losses which are dominant constituent of net Q-factor observed in experiments due to encapsulation of uncapped drumhead resonator. Essentially, the geometry of the capped resonator constitutes upper and lower cavities subjected to fluid-structure interaction losses on both sides of the annular plate. The dominant fluid-structure interaction loss is found to be due to squeezing action acting simultaneously in the upper and lower cavities. However, as we go to the higher modes, squeeze film damping become very small and the damping due to structure related losses such as clamping and thermoelastic losses becomes significant. We found the thermoelastic damping to be the dominant source of structural damping at higher resonant modes, whereas, the clamping losses are found to be relatively smaller. Finally, on comparing the net quality factor with the experimental results, we observed that the squeeze film losses are dominant at lower frequencies, and thermoelastic losses dominate at the higher frequencies. However, there remains some discrepancy between theoretical and experimental Q-factors particularly over higher frequency range. Such discrepancy may be due to some unaccounted factors which may be explored to improve the modeling of damping in capped resonators. The emphasis of this work has been towards developing a comprehensive understanding of different dominant dissipative mechanisms, classified into the fluid-structure interaction and the structural losses, that are constituent of the Q-factor at various resonant modes of uncapped and capped drumhead resonators.

Different methods for the determination of cantilever properties in non-contact atomic force microscopy (NC-AFM) are under investigation. A key aspect is the determination of the cantilever stiffness being essential for a quantitative NC-AFM data analysis including the extraction of the tip-surface interaction force and potential. Furthermore, a systematic analysis of the displacement noise in the cantilever oscillation detection is performed with a special focus on the thermally excited cantilever oscillation. The propagation from displacement noise to frequency shift noise is studied under consideration of the frequency response of the PLL demodulator. The effective Q-factor of cantilevers depends on the internal damping of the cantilever as well as external influences like the ambient pressure and the quality of the cantilever fixation. While the Q-factor has a strong dependence on the ambient pressure between vacuum and ambient pressure yielding a decrease by several orders of magnitude, the pressure dependence of the resonance frequency is smaller than 1% for the same pressure range. On the other hand, the resonance frequency highly depends on the mass of the tip at the end of the cantilever making its reliable prediction from known cantilever dimensions difficult. The cantilever stiffness is determined with a high-precision static measurement method and compared to dimensional and dynamic methods. Dimensional methods suffer from the uncertainty of the measured cantilever dimensions and require a precise knowledge its material properties. A dynamic method utilising the measurement of the thermally excited cantilever displacement noise to obtain cantilever properties allows to characterise unknown cantilevers but requires an elaborative measurement equipment for spectral displacement noise analysis. Having the noise propagation in the NC-AFM system fully characterised, a proposed method allows for spring constant determination from the frequency shift noise at the output of the PLL demodulator with equipment already being available in most NC-AFM setups.